Problem: Solve for $x$ and $y$ using substitution. ${5x-4y = -10}$ ${y = -x+7}$
Solution: Since $y$ has already been solved for, substitute $-x+7$ for $y$ in the first equation. ${5x - 4}{(-x+7)}{= -10}$ Simplify and solve for $x$ $5x+4x - 28 = -10$ $9x-28 = -10$ $9x-28{+28} = -10{+28}$ $9x = 18$ $\dfrac{9x}{{9}} = \dfrac{18}{{9}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {y = -x+7}\thinspace$ to find $y$ ${y = -}{(2)}{ + 7}$ $y = -2 + 7$ $y = 5$ You can also plug ${x = 2}$ into $\thinspace {5x-4y = -10}\thinspace$ and get the same answer for $y$ : ${5}{(2)}{ - 4y = -10}$ ${y = 5}$